Time series are highly valuable and rarely shareable across nodes, making federated learning a promising paradigm to leverage distributed temporal data. However, different sampling standards lead to diverse time granularities and variable sets across nodes, hindering classical federated learning. We propose PiXTime, a novel time series forecasting model designed for federated learning that enables effective prediction across nodes with multi-granularity and heterogeneous variable sets. PiXTime employs a personalized Patch Embedding to map node-specific granularity time series into token sequences of a unified dimension for processing by a subsequent shared model, and uses a global VE Table to align variable category semantics across nodes, thereby enhancing cross-node transferability. With a transformer-based shared model, PiXTime captures representations of auxiliary series with arbitrary numbers of variables and uses cross-attention to enhance the prediction of the target series. Experiments show PiXTime achieves state-of-the-art performance in federated settings and demonstrates superior performance on eight widely used real-world traditional benchmarks.
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